What are some strategies for solving limit problems involving zero or infinity?

In summary, the conversation discusses three limit problems for a homework assignment. The first two problems involve evaluating limits as x approaches a specific value, with potential challenges such as the top and bottom both approaching zero or the exponent becoming (1/0). The third problem involves a limit as x approaches infinity. The person also mentions needing tips or clarification for the third problem.
  • #1
gsxrK3
4
0
Hello. I have a couple limit problems for my homework and I'm not sure what to do with them.

1. lim x->0 of (a^x - b^x)/x = ?

I see that as x goes to zero, the top goes to 1-1 which would make the whole thing zero, but at the same time the bottom goes to 0 but you can't divide by zero of course. I'm not sure if I'm supposed to do some voodoo to remove the x from the bottom, or if there's some concept I should explain. Maybe I need to use the definition of a limit somehow?

2. lim x->9 of (1-x)^(1/x). Again the same type of situation. 1^(anything) is 1, but at the same time the exponent is going to (1/0).

There is also a third problem. If there is something different I need to know about this I would appreciate some tips, but if you think I can get it once I learn the previous two then never mind it.

3. lim x->infinity [sqrt(x)logx]/x

Thank you,
gsxrk3
 
Physics news on Phys.org
  • #2
lhopital...sorry for the stupid question.
 

1. What are "A Couple Limit Problems"?

"A Couple Limit Problems" are mathematical problems that involve finding the limit of a function as a variable approaches a specific value. These problems are used to model real-world situations and help in predicting future trends or outcomes.

2. How do you solve a couple limit problem?

To solve a couple limit problem, you need to first plug in the given value of the variable into the function. Then, you can use algebraic techniques such as factoring, rationalization, or substitution to simplify the expression. Finally, you can evaluate the limit by plugging in the value of the variable and solving the resulting expression.

3. What is the importance of understanding couple limit problems?

Understanding couple limit problems is important for many reasons. They are used in various fields such as physics, engineering, economics, and finance to model and predict real-world situations. They also help in developing critical thinking and problem-solving skills.

4. What are some common techniques used to solve couple limit problems?

Some common techniques used to solve couple limit problems include factoring, rationalization, substitution, and L'Hopital's rule. These techniques help in simplifying the expressions and evaluating the limit more easily.

5. How can I practice and improve my skills in solving couple limit problems?

The best way to practice and improve your skills in solving couple limit problems is by solving a variety of problems regularly. You can also seek help from online resources, textbooks, or a tutor to understand different techniques and approaches to solving these problems. Additionally, practicing with real-world examples can help in understanding the practical applications of these problems.

Similar threads

I A question about limits and infinity
    • Calculus
Replies
7
Views
1K
I What's my mistake in this integration problem?
    • Calculus
Replies
8
Views
415
I Some questions on l'Hôpital rules
    • Calculus
Replies
9
Views
2K
MHB Find the limit as x goes to infinity
    • Calculus
Replies
5
Views
2K
I Express the limit as a definite integral
    • Calculus
Replies
16
Views
2K
I Explanation and clarifications in epsilon-delta limit proofs
    • Calculus
Replies
4
Views
1K
MHB Limit involving a hyperbolic function
    • Calculus
Replies
4
Views
1K
I Proving limit theorems when limit tends to infinity
    • Calculus
Replies
7
Views
2K
I Multivariable limits - path problem
    • Calculus
Replies
3
Views
2K
B Some questions regarding the integral of cos(ax), "a" not zero
    • Calculus
Replies
16
Views
1K

Hot Threads

Recent Insights

Back
Top